Date of Award:

5-2007

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Advisor/Chair:

Dariusz Wilczynski

Abstract

In order to enlarge the class of equations provided by traditional polynomials over a binary algebra A to a more useful class of equations, we introduce polynomials in noncommuting or nonassociating indeterminates. We discuss algebraic properties of these formal polynomial algebras and their accompanying polynomial function algebras. We present certain basis results for polynomial algebras, which are used to address the question of zero divisors in a polynomial algebra. We give an analog of the remainder theorem and the factor theorem for polynomials. Particular emphasis is placed on showing the difference between polynomials and polynomial functions. We also provide a brief discussion of polynomial composition and formal derivatives.

Checksum

4b5b7b470482bce6aa484a20084e0b48

Included in

Mathematics Commons

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